A196104 Repdigit semiprimes (semiprimes composed of identical digits).

4, 6, 9, 22, 33, 55, 77, 111, 1111, 11111, 1111111, 11111111111, 11111111111111111, 2222222222222222222, 3333333333333333333, 5555555555555555555, 7777777777777777777, 22222222222222222222222, 33333333333333333333333, 55555555555555555555555

Offset

1,1

Comments

A semiprime can be repdigit (base 10) in only three ways. It can be a single-digit semiprime, a repunit semiprime (A102782), or a repunit prime times a prime digit {2, 3, 5, 7}. Occurs in proof that the sequence is infinite in which a(n) is the least semiprime > a(n-1) such that a(n) has no digit in common with a(n-1). - Jonathan Vos Post; corrected by Max Alekseyev, Sep 14 2022

Links

Max Alekseyev, Table of n, a(n) for n = 1..35

Formula

Union of {4, 6, 9}, A102782, 2*A004022, 3*A004022, 5*A004022, and 7*A004022. - Jonathan Vos Post and R. J. Mathar, Oct 27 2011

Example

a(12) = 11111111111 = 21649 * 513239 is semiprime.

Maple

with(numtheory):for n from 1 to 23 do:for b from 1 to 9 do:x:=(((10^n)- 1)/9)*b:if bigomega(x)=2 then printf(`%d, `, x):else fi:od:od:

Mathematica

Select[FromDigits/@Flatten[Table[PadRight[{}, i, n], {i, 25}, {n, 9}], 1], PrimeOmega[ #] ==2&] (* Harvey P. Dale, Mar 11 2019 *)

Prog

(PARI) print1("4, 6, 9"); for(n=1, 20, t=10^n\9; if(bigomega(t)==2, print1(", "t)); if(isprime(t), forprime(p=2, 7, print1(", "p*t)))) \\ Charles R Greathouse IV, Oct 27 2011

Crossrefs

Subsequence of A046328.

Except for initial terms, subsequence of A116063.

Cf. A000042, A001358, A004023, A046413, A102782.

Sequence in context: A118690 A084994 A046328 * A046376 A229129 A272436

Adjacent sequences: A196101 A196102 A196103 * A196105 A196106 A196107

Keyword

nonn,base

Author

Michel Lagneau, Oct 27 2011

Extensions

Edited by Max Alekseyev, Sep 14 2022

Status

approved